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Proof step 6 from proof fermat-pos (previous step)

i = i1 + 1, ≡mod(i1 ^ j, i1, j), 0 < i, prime(j), ∀ i0, j. i→n(i0) < i→n(i) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ ≡mod(i ^ j, i, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
prime(j), ≡mod(i1 ^ j, i1, j), 0 ≤ i1, ∀ i0, j. i→n(i0) < i→n(i1 + 1) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ ≡mod((i1 + 1) ^ j, i1 + 1, j)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs